While Google's policies raise concerns, in the US, the Patriot Act requires both Bing and Google to retain way more information about searches than necessary, and both search engines have a strong incentive to make money off of search by targeting ads, which is most effectively done by tracking and building profiles on users. They don't need to know your name, but they'll want to know what user #23451247 is interested in, what his/her kinks are, how to persuade user #23451247 to buy stuff, and they'll want to sell that information to advertisers, who can then correlate that profile with profiles from elsewhere that will allow a name to be attached.